Langmuir, 2016, 32 (39), pp 10083 10092 DOI: Received 21 August …20et%20al... · 2019-12-16 · Langmuir, 2016, 32 (39), pp 10083–10092 DOI: 10.1021/acs.langmuir.6b03098 Received

Langmuir, 2016, 32 (39), pp 10083–10092

DOI: 10.1021/acs.langmuir.6b03098 Received 21 August 2016

Published online 7 September 2016

Published in print 4 October 2016

Lipid spontaneous curvatures estimated from temperature-dependent

changes in inverse hexagonal phase lattice parameters: the effects of metal

cations

Marcus K. Dymond1*, Richard J. Gillams2, Duncan J. Parker2, Jamie Burrell2, Ana Labrador3, Tommy

Nylander4, George S. Attard2*

1 Division of Chemistry, School of Pharmacy and Biomolecular Sciences, University of Brighton,

Brighton, BN2 4GJ, UK

2 Chemistry, Faculty of Natural & Environmental Sciences, University of Southampton, Southampton

SO17 1BJ, UK

3 MAX IV Laboratory, Lund University, PO Box 118, SE-221 00, Lund, Sweden

4 Physical Chemistry, Lund University, PO Box 124, SE-221 00, Lund, Sweden

(*) Authors for correspondence: [email protected]; [email protected]

mailto:[email protected]

mailto:[email protected]

Langmuir, 2016, 32 (39), pp 10083–10092




Abstract

Recently we reported a method for estimating the spontaneous curvatures of lipids from

temperature dependent changes in the lattice parameter of inverse hexagonal liquid crystal phases

of binary lipid mixtures. This method makes use of 1,2-dioleoyl-sn-glycerol-3-phosphoethanolamine,

(DOPE) as a host lipid, which preferentially forms an inverse hexagonal phase, to which a guest lipid

of unknown spontaneous curvature is added. The lattice parameters of these binary lipid mixtures

are determined by small angle X-ray diffraction at a range of temperatures and the spontaneous

curvature of the guest lipid is determined from these data. Here we report the use of this method on

a wide range of lipids under different ionic conditions. We demonstrate that our method provides

spontaneous curvature values for DOPE, cholesterol and monoolein that are within the range of

values reported in the literature. Anionic lipids 1,2-dioleoyl-sn-glycerol-3-phosphatidic acid (DOPA)

and 1,2-dioleoyl-sn-glycerol-3-phosphoserine (DOPS) were found to exhibit spontaneous curvatures

that depend on the concentration of divalent cations present in the mixtures. We show that the

range of curvatures estimated experimentally for DOPA and DOPS can be explained by a series of

equilibria arising from lipid-cation exchange reactions. Our data indicate a universal relationship

between the spontaneous curvature of a lipid and the extent to which it affects the lattice

parameter of the hexagonal phase of DOPE when it is part of a binary mixture. This universal

relationship affords a rapid way of estimating the spontaneous curvatures of lipids that are

expensive, only available in small amounts or are of limited chemical stability.

Langmuir, 2016, 32 (39), pp 10083–10092




Introduction

Membrane curvature, curvature elastic stress and stored elastic energy are continuum properties

dependent on the spontaneous curvature (c0) of the lipids that comprise the bilayer. The

spontaneous curvature is a material parameter, which corresponds to the curvature that an

unconstrained monolayer of a lipid would adopt. This has been shown to play a critical role in the

energetics of many of the lipid-protein interactions that occur in biological membranes 1,2. For

example, curvature elastic stress, which arises from a system being forced to adopt a curvature that

is different from c0, has been shown to modulate the activity of many membrane interacting

proteins 3,4 and drives the folding of other membrane bound proteins 5,6. These observations

underpin the intrinsic curvature hypothesis, which postulates that cells regulate the composition of

their biological membranes so that the net curvature elastic stress is under homeostatic control 7–10.

This has led to the proposal that the antineoplastic activity of some types of amphiphilic compounds

could be mediated by their effect on membrane curvature elastic stress 11,12. Lipids and lipid

membranes are key to a range of biological processes and it therefore seems likely that membrane

elastic properties – and hence the spontaneous curvatures of particular lipids are crucial for these

processes. Thus determination of spontaneous curvature in relation to lipid composition could help

in furthering our understanding of a range of pathologies, such as cancer 13, Alzheimer’s disease 14

and obesity 15, that involve lipid disorders.

Several theoretical models to describe the physics of biological membrane assembly have

been proposed 16. To investigate quantitatively whether or not particular biological processes are

controlled or mediated by curvature elastic stress requires estimates of the spontaneous curvatures

of the lipids that comprise the membrane. Typically, quantification of stored elastic energy uses

small angle X-ray scattering (SAXS) to determine the spontaneous curvature of pure lipids. These

methods involve studying lipids in the inverse hexagonal lyotropic liquid crystal phase (HII) to

determine the radius of curvature at the neutral plane of the lipid molecules at zero osmotic stress

17, and this is defined as the spontaneous curvature of that lipid. It should be noted however that in

practice many studies determine c0 at the pivotal plane due to this being easier to achieve

experimentally 18–20 and in this manuscript we discuss all spontaneous curvatures as measured at the

pivotal plane, unless otherwise noted. Lipids that do not ordinarily form HII phases but which have

negative spontaneous curvatures, albeit weak, can be induced to form HII phases by the addition of

long chain liquid hydrocarbons to relieve packing frustration. Binary lipid mixtures comprising a well-

characterized HII phase forming lipid (the host) and a guest lipid with unknown c0 have been used to

determine the spontaneous curvature of the guest lipid from changes in the lattice dimensions of

Langmuir, 2016, 32 (39), pp 10083–10092




the phase as the concentration of guest molecules increases 21–24. Using this methodology and other

related scattering techniques 18,25 values for the spontaneous curvatures of a number of biologically

relevant lipids have been reported. Although these experimental approaches to determining c0 are

well established26,27, they involve lengthy experiments and require significant amounts of sample

(typically > 100 mg). Consequently c0 values have been documented for only a small number of

lipids, mainly those that are most easily available, out of the rich diversity of lipid species that exist

across the different domains of life. Even for the more common lipid species, there is a paucity of c0

values in the presence of buffers, other ionic species or as a function of pH, but such data as are

available show significant ionic effects. For example the spontaneous curvature of 1,2-dioleoyl-sn-

glycero-3-phosphoserine (DOPS) is pH dependent 24 and the spontaneous curvature of 1,2-dioleoyl-

sn-glycero-3-phosphatidic acid (DOPA) and lyso 1-oleoyl-2-hydroxy-sn-glycero-3-phosphatidic acid

(OPA) are dependent on the surrounding divalent cation concentration 28,29.

In our recent work 30, in which we reported the formation of Fd3m inverse cubic phases in

binary mixtures of oleic acid (OA) with 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) or

1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), we described a new way of estimating the

spontaneous curvatures of lipids. This method made use of the temperature-induced lattice

expansion of the HII phase in a host-guest binary system using frustrated lipid mixtures. The

advantages of our method of estimating c0 are the speed with which data can be obtained and the

relatively small amounts (< 1 mg) of lipids needed. However the extent to which the method is

applicable to a wide range of lipid systems, and in particular to anionic lipids in the presence of

divalent cations, is not known. Here we report data from a systematic application of our method to a

selection of structurally diverse lipids, and to anionic lipids in media that contain divalent cations,

and validate the range of applicability of our experimental methodology.

Experimental

DOPE, 1,2-phytanyl-sn-glycero-3-phosphoethanolamine (DiPhyPE), DOPS and DOPA were

purchased from Avanti Polar Lipids (Alabama USA). Trans-retinoic acid (tRA), trans-retinal (tR) and

cis-retinal (cR), calcium chloride, cholesterol (chol), monoolein (MO), magnesium chloride,

chloroform and bis-tris were purchased from Sigma-Aldrich (UK). Trans, trans-2,4-decanedienal (DD)

and cis-11-hexadecenal (HD) were purchased from Tokyo Chemical Industry UK Ltd. Ultrapure water

of 18.2 mΩ conductivity (Barnstead Nanopure Diamond) was used for the preparation of all samples.

Langmuir, 2016, 32 (39), pp 10083–10092




Lipid samples were analyzed in pure water and three different buffer solutions with varying

concentrations of divalent cations [M2+]; low divalent cation buffer (13 mM [M2+]) (bis tris 150 mM,

10 mM MgCl2 and 3 mM CaCl2 at pH 7.0), medium divalent cation buffer (65 mM [M2+]) (bis tris 150

mM, 50 mM MgCl2 and 15 mM CaCl2 at pH 7.0) and high divalent cation buffer (130 mM [M2+]) (bis

tris 150 mM, 100 mM MgCl2 and 30 mM CaCl2 at pH 7.0).

Preparation of lyotropic liquid crystal phases for X-ray measurements

Binary lipid samples were prepared by weighing dry quantities of DOPE (used as received), typically

in the range of 50 to 100 mg, into 500 µl microcentrifuge tubes. Smaller amounts of the secondary

lipid (0.005 to 0.09 mole fractions) were prepared by adding microlitre volumes of lipid solutions,

with known concentration, dissolved in HPLC grade chloroform. A further 200 μl of chloroform was

added to each sample and the dissolved lipids were mixed by vortexing before being dried overnight

in vacuo.

The moisture content of the lipids was estimated to be ≤0.1% w/w, leading to an uncertainty in the

lipid composition of the mixtures of up to 2 %.

To prepare lyotropic liquid crystal preparations in excess of limiting hydration, 100 µl of pure water

or one of the buffer solutions was added to each dry lipid sample. All samples were mixed manually

using a small spatula for several minutes prior to centrifugation at 17000 g (Heraeus Pico 17

Centrifuge) for 5 minutes. Manual mixing and centrifugation cycles were repeated three times

before samples were incubated at 37°C for 2-3 days. Prior to data collection a further manual mixing

and centrifugation cycle was carried out.

Small angle X-ray diffraction (SAXD) studies

SAXD studies were performed at the SAXS station I911-4 of the MAX IV Synchrotron, Lund,

Sweden, extensive details of the experimental setup have been published previously 30,31. Figure S1

shows a representative SAXD image and Table S1 provides the lattice parameter data for all the

samples we have analyzed.

Equilibrium association modelling

Langmuir, 2016, 32 (39), pp 10083–10092




Equilibrium association models for anionic lipids and metal cations were simulated using

COPASI 4.11 (Build 65), which is a simulator for biochemical networks. Reactions were modelled in a

single compartment based on the following dissociation phenomena: MX2 ⇌ M2+ + 2X- (dissociation

of a divalent metal cation salt e.g. MgCl2), NaX ⇌ Na+ + X- (dissociation of a sodium salt e.g. NaCl),

LNa ⇌ L- + Na+ (dissociation of sodium salt of anionic lipid), LM+ ⇌ L- + M2+ and L2M ⇌ L- + LM+

(dissociation of divalent cation salts of anionic lipids). Equilibrium association constants were

calculated from the ratio of the association and dissociation reaction rates. Equilibrium

concentrations of the lipid species LNa, L2M, LM+ and L- were used to calculate the spontaneous

curvatures of mixtures across the range of compositions that were investigated experimentally and

these values were compared with the experimental data. Rate constants for the association and

dissociation reactions were adjusted iteratively to minimize the variance between the calculated

values of c0 for all the mixtures studied and experimental values.

Results and discussion

Lattice parameters were calculated from SAXD data obtained from the HII phases of a wide range of

binary mixtures comprising DOPE and low concentrations (typically mole fractions ranging from 0.03

to 0.09) of a second guest lipid over the temperature range 27°C to 57°C. This method uses

frustrated HII phases and assumes that c0 mix and do not change with temperature, whereas in fact

these parameters show weak temperature dependence 21,32,33 . The method also assumes that of

the host lipid is unaffected by the small amounts of guest lipid present in the mixtures 3.

Spontaneous curvatures of guest lipids from host hexagonal phase dimensions

As we described previously 30, the change in lattice parameters of frustrated inverse hexagonal

lyotropic phases observed by SAXD at different temperatures, can be used to obtain estimates of the

spontaneous curvature of lipid mixtures (c0 mix) and their component lipid species. The reasoning

behind the method stems from the observation that the stored elastic energy in an inverse

hexagonal cylinder of lipids increases as the principal curvature of the mixture deviates away from

the spontaneous curvature of the lipid mixture (c0 mix). The method is only applicable to composition

ranges where there is a single lyotropic phase 30; a full derivation is provided in the Supporting

Information.

Langmuir, 2016, 32 (39), pp 10083–10092




In summary, for an ideal mixture of amphiphiles in the inverse hexagonal phase, the

curvature c1 = 1/R1 (where R1 is the radius of curvature measured from the center of the water filled

hexagonal cylinder to the radius of the pivotal plane (Rp) 22 i.e. the plane on which the area per lipid

molecule is not changed upon applying a bending moment) is related to the spontaneous curvature

of the mixture (c0 mix) through the following expression,

1

2{(𝑐1

(𝐴))

2− (𝑐1

(𝐵))

2} = 𝑐0 𝑚𝑖𝑥 {𝑐1

(𝐴)− 𝑐1

(𝐵)} +

Δ𝐸𝑇

𝜅 (1)

where ΔET is the difference in stored elastic energy between the two temperatures and is the

bilayer bending elastic modulus. A plot of 1

2{(𝑐1

(𝐴))

2− (𝑐1

(𝐵))

2} against {𝑐1

(𝐴)− 𝑐1

(𝐵)} for pairs of

temperatures (A and B), gives a straight line, where the intercept of this line is equal to Δ𝐸𝑇

𝜅 and the

slope is equal to the spontaneous curvature of the mixture, c0 mix. Using the lattice parameters (Lp) of

the binary lipid system data obtained by SAXD, c1(A) and c1

(B) can be obtained since the inter-pore

spacing dl (equal to the lattice parameter for the HII phase) at temperature A is related to c1(A) as

follows:

𝑑𝑙(𝐴)

= 2𝑅𝑤(𝐴)

+ 2𝑙(𝐴) (2),

where Rw(A) is the radius of the water cylinder in the HII phase and l(A) is the lipid length, both at

temperature A, and

1

𝑐1(𝐴) = 𝑅𝑝

(𝐴)= 𝑅𝑤

(𝐴)+ 𝑙𝑥

(𝐴)= (

𝑑𝑙(𝐴)

2) − 𝑙𝑦

(𝐴) (3),

where

𝑙(𝐴) = 𝑙𝑥(𝐴)

+ 𝑙𝑦(𝐴)

(4),

lx is the distance from the pivotal plane to the edge of the water pore and ly is the distance from Rp

to the edge of the hydrocarbon cylinder as summarized in Figure S2. For the small changes in dl, that

occur at different temperatures, lx or ly is not expected to change significantly relative to Rw, hence

Rp, at different temperatures, can be estimated from Eq. 3. Using independent structural data

obtained for the inverse hexagonal phase of DOPE at 25°C (which is the closest published data

Langmuir, 2016, 32 (39), pp 10083–10092




available to our starting temperature of 27°C), we estimate the value of ly to be 0.835 nm, since Rw =

2.11 nm and 2l = 3.15 nm 34 and for an unstressed hexagonal cylinder R0 ≈ Rp and thus c0 = c1.

In our original estimate 30 we used the published value of c0 for DOPE of -0.435 nm-1 35

(measured at the pivotal plane) to determine ly. This is at the extreme of reported values of the

spontaneous curvature of DOPE in water (all measured at the pivotal plane unless otherwise stated),

which range from -0.399 ± 0.005 nm-1 21 using tricosene measured at the neutral plane, -0.351 nm-1

22, -0.333 nm-1 24 to -0.348 nm-1 using tetradecane36. Studies of the spontaneous curvature of DOPE in

different buffers and salts yield c0 values of -0.370 nm-1 (25 mM Mes, 25 mM Tes at pH 7), -0.435 nm-

1 (25 mM Mes, 25 mM Tes at pH 7, 150 mM NaCl) and -0.456 nm-1 (25 mM Mes, 25 mM Tes at pH 7,

150 mM NaCl, 25 mM CaCl2) utilizing tetradecane 20. Investigation of the effect of temperature and

calcium cations in the buffer HEPES (10 mM), utilizing tetradecane has shown that the range of c0 for

DOPE extends from -0.331 nm-1 to -0.374 nm-1 32 at the pivotal plane. In this publication we use the

value of c0 for DOPE of -0.351 nm-1 to determine ly, which is intermediate in the range of DOPE c0

values reported in the literature and the radius of the pivotal plane of inverse hexagonal cylinders of

DOPE in water at 25°C. Therefore, whilst our method assumes c0 is temperature independent, it

effectively estimates the value of c0 at the pivotal plane at 25°C, since it is parameterized at this

temperature.

To estimate the spontaneous curvature of the guest lipid (j) in the DOPE host matrix, we

assume ideal mixing of the components and that c0 for a mixture (c0 mix) is the average of the c0

values of its components, weighted by their mole fractions 3,37. Such that,

𝑐0 𝑚𝑖𝑥 = 𝑥𝑐0𝐷𝑂𝑃𝐸 + (1 − 𝑥)𝑐0𝑗 (5).

Where we have calculated c0j in buffers other than water, we initially determine the c0 of

DOPE in that buffer using the method by fitting to Eq.1 to calculate c0j For all c0 determinations, we

conducted lattice parameter measurements at six different temperatures and in fitting the data to

Eq. 1 we used all unique combinations of temperature pairs. For linear fits to Eq. 1, this approach

yields R2 values, approaching 1.The error in the calculation of c0 mix therefore stems principally from

error in the lattice parameter measurements which is dominated the accuracy of the measured lipid

compositions (up to 2%, as discussed in the experimental section). We estimate that overall the

precision of the method yields an error in c0j of ± 5 to 10%, depending on the amount of

incorporated lipid and apply an intermediate error value of ± 7.5 % to all c0j values in Tables 1 and 2.

The accuracy of our measurements i.e. the proximity of the c0 mix values that emerge from our

Langmuir, 2016, 32 (39), pp 10083–10092




calculations when compared to literature values is dependent on two key assumptions. The first is

that the value of ly and lx does not change over the temperature range studied and the second is that

ly and lx do not change over the composition range studied. As discussed these statements are not

explicitly true but as we have noted previously lx changes by less than 2% w.r.t. the changing radius

of water cylinders in DOPC: DOG 30 inverse hexagonal phases and similar arguments have been

presented for the dependence of DOPE phases with temperature 38 and composition 20,22,24.

The spontaneous curvatures of guest lipids in host DOPE inverse hexagonal phases

The lattice parameters for the inverse hexagonal phases used to obtain c0 mix are

provided in the Supporting Information, Table S1 and the c0j values for the individual guest lipid are

shown in Table 1 . The first thing to note is that the coefficient of variance (standard deviaton/ mean

c0j, expressed as a percentage) when calculated for the each lipid in Table 1 is typically in the range

of 5 to 10%. This demonstrates that the previously estimated 5 to 10% error in c0j is appropriate.

lipid j Mf j (in DOPE)

c0j / nm-1 c0j error

(±) mean

c0j s.d.

chol

0.05 -0.54 0.04

-0.47 0.05 1 -0.46 0.03

3 -0.44 0.03

5 -0.45 0.03

MO

1 -0.56 0.04

-0.54 0.03 2 -0.55 0.04

3 -0.51 0.04

diPhyPE

3 -0.67 0.05

-0.65 0.02 6 -0.65 0.05

9 -0.63 0.05

OA

2 -0.69 0.05

-0.71 0.03 3 -0.70 0.05

4 -0.75 0.06

cR

3 -1.08 0.08

-1.13 0.06 6 -1.12 0.08

9 -1.20 0.09

DD

5 -0.61 0.05

-0.63 0.05 20 -0.58 0.04

30 -0.69 0.05

HD

5 -0.52 0.04

-0.52 0.04 20 -0.47 0.04

30 -0.56 0.04

Langmuir, 2016, 32 (39), pp 10083–10092




tR

3 -0.87 0.07

-1.05 0.16 6 -1.20 0.09

9 -1.06 0.08

tRA 6 -0.65 0.05

-0.63 0.04 9 -0.60 0.05

Table 1 spontaneous curvature data, c0j ± 7.5% error, for guest lipids in an inverse hexagonal DOPE

host phase and excess water, where s.d. is the standard deviation of the mean c0j and Mfj is the mole

fraction of lipid j in DOPE. Table S2 provides further details of c0 mix (i.e. the gradient determined

from Eq. 1) and the individual R0 and c0 values for each sample analyzed. All c0j determinations are at

the pivotal plane.

Previous studies have shown that divalent cations have only minor effects on the structural

properties of the inverse hexagonal phases of zwitterionic lipids such as DOPE 20, with c0 measured

at the pivotal plane increasing from -0.33 nm-1 in water to -0.35 nm-1 in 100 mM calcium chloride

(10mM HEPES pH 7.2)32. Therefore to confirm the accuracy of the c0 values that we estimate by our

method we determined c0 at the pivotal plane for DOPE in each of the buffers containing divalent

cations, our results were in the range of -0.37 to -0.36 nm-1 for 13 mM, 65 mM and 130 mM [M2+]

and in good agreement with the values in the literature.

The c0 of cholesterol, at the pivotal plane, has been reported in the literature as -0.435 nm-1

in water 39, using tetradecane, and as -0.49 ± 0.01 nm-1 21 at the neutral plane and 35°C in water.

From our data, the decrease in lattice parameter with increasing cholesterol content (Table S1) is

consistent with cholesterol having a smaller radius of spontaneous curvature than DOPE. These

lattice parameter data, in conjunction with our method, gives a range of c0 values for cholesterol

from -0.54 to -0.44 nm-1 with a mean c0 for all mixture compositions of -0.47 ± 0.05 nm-1, which is

within the range of literature values. The spontaneous radius of curvature of MO has previously

been reported as -2.00 ± 0.03 nm 40 at the pivotal plane, which corresponds to c0 of -0.50 nm-1, our

method estimates c0 to be a comparable value of -0.54 ± 0.03 nm-1.

We also used our previous data for OA in DOPE, together with the c0 for DOPE we use here, to re-

estimate c0 for OA monomers at the pivotal plane, which works out as -0.71 ± 0.03 nm-1; as discussed

previously 30 this is consistent with literature values41.

Langmuir, 2016, 32 (39), pp 10083–10092




The good agreement between the c0 values from our experiments and values reported in the

literature for these very different lipids gives some confidence that our method of estimating c0 is

robust and applicable to a wide range of lipid structures. Moving away from well-characterized

systems we were able to determine the spontaneous curvature of diPhyPE (c0 = -0.65 ± 0.03 nm-1).

Given the wider cross-sectional area of the phytanyl chain, when compared to the oleoyl chain, this

increase in spontaneous curvature relative to DOPE is consistent with expectations. Since OA has a

significant negative spontaneous curvature we wondered whether long-chained aldehydes would

also be type II lipids. From our SAXD data we estimate c0 values for DD and HD to be -0.63 ± 0.05 nm-

1 and -0.61 ± 0.16 nm-1 respectively, which are comparable to the c0 value of OA. The type II

characteristics of fatty acids and fatty aldehydes appear to be consistent across a diversity of

molecular structures as shown by the c0 values we estimated cR (-1.13 ± 0.06 nm-1), tR (-1.05 ± 0.16

nm-1) and tRA (-0.63 ± 0.04 nm-1).

The spontaneous curvatures of anionic lipids in host DOPE inverse hexagonal phases

One of the most challenging issues in evaluating the role of stored elastic energy in

mediating biological processes in vivo is disentangling the extent to which anionic lipid activation of

some membrane proteins is driven by electrostatic forces rather than membrane stored elastic

energy. This question is complicated to answer as the salts used in buffers for assaying enzyme

activity might also effect on the spontaneous curvatures of anionic lipids. Literature values of the

spontaneous curvature of DOPS highlight the sensitivity of c0 to the ionic environment experienced

by the anionic lipid. Detailed studies 24 show that at pH 7 the spontaneous curvature of DOPS is

+0.069 nm-1, whilst at pH 2, where the anionic DOPS molecules are protonated, c0 has been

observed to be -0.435 nm-1. Interestingly the presence of tetradecane appears to affect the degree

of protonation of DOPS, driving it into flat lamellar sheets, rather than promoting the formation of

curvature relaxed inverse hexagonal phases. This implies that the DOPS molecules are somewhat

deprotonated in tetradecane containing systems 24. This can be explained as an effect of the

tetradecane solubilised in the lipid layer and hence increasing the distance between the ionizable

groups. This in turn reduces the repulsive electrostatic potential between the head groups and

hence facilitates deprotonation.

Langmuir, 2016, 32 (39), pp 10083–10092




Consequently the c0 of DOPS is expected to depend on the anionic lipid concentration in

binary mixtures with DOPE. At low DOPS mole fractions the average separation between anionic

lipid molecules is sufficiently large that the contribution of electrostatic repulsion to spontaneous

curvature will be principally driven by molecular shape. However as DOPS mole fraction increases

electrostatic repulsion will play an increasingly significant role in determining c0. While there is some

evidence of this trend in the literature 42, the presence of metal cations can confound this effect. The

presence of monovalent cations will act to screen headgroup charge 43 and divalent cations that

associate strongly with the headgroups will promote the formation of DOPS dimers, bridged by the

divalent metal, which are strongly type II lipids 44. These competing mechanisms, underpinned by

association constants of different magnitudes, generic to anionic lipids, have been reported for

systems like DOPA 20 and 1,2-dioleoyl-sn-glycero-3-phosphoglycerol (DOPG) 45. We therefore set out

to determine how spontaneous curvature of DOPS and DOPA in DOPE inverse hexagonal phases

changes in the presence of buffers with different concentrations of divalent cations [M2+].

Table 2 shows that DOPS has a negative spontaneous curvature in buffers with different

concentrations of divalent cations. However, unlike the case of zwitterionic or uncharged lipids, the

c0 of DOPS appears to change as a function of its concentration in the binary mixture, ranging from -

0.50 nm-1 to -0.14 nm-1. This is indicated because the coefficient of variance (cv) in some of these

studies is in excess of the 10% tolerance previously identified. For example in DOPS 13 mM divalent

cations the cv is 19%, similarly in DOPA 65 mM divalent cations the cv of DOPA is 23%.

lipid j [M2+]/

mM Mf j (in DOPE)

c0j / nm-1 c0j error (±)

DOPE

0 0 -0.37 0.03

13 0 -0.37 0.03

65 0 -0.36 0.03

130 0 -0.36 0.03

DOPS 0

3 -0.41 0.03

6 -0.35 0.03

9 -0.26 0.02

DOPS 13 3 -0.41 0.03

Langmuir, 2016, 32 (39), pp 10083–10092




6 -0.22 0.02

9 -0.14 0.01

DOPS 65

3 -0.43 0.03

6 -0.41 0.03

9 -0.49 0.04

DOPS 130

3 -0.42 0.03

6 -0.43 0.03

9 -0.42 0.03

DOPA 0

3 -0.43 0.03

6 -0.42 0.03

9 -0.34 0.03

DOPA 13

3 -0.42 0.03

6 -0.36 0.03

9 -0.31 0.02

DOPA 65

3 -0.42 0.03

6 -0.58 0.04

9 -0.68 0.05

DOPA 130

3 -0.45 0.03

6 -0.54 0.04

9 -0.54 0.04

Table 2 spontaneous curvature data, c0j ± 7.5% error, for guest lipids in an inverse hexagonal DOPE

host phase and excess water. Mfj is the mole fraction of lipid j in DOPE and [M2+] is the total divalent

cation concentration. Table S3 provides further details of c0 mix (i.e. the gradient determined from Eq.

1) and the individual R0 and c0 values for each sample analyzed. All c0j determinations are at the

pivotal plane.

Figure 1A, shows that in the case of samples containing water or 13 mM [M2+] buffer, at limiting

hydration, the estimated c0 of DOPS initially decreases, and then increases as the amount of DOPS in

DOPE increases, going through a minimum at ~3 mole %.

In the buffers with 65 mM and 130 mM divalent cations, Figure 1B, the c0 of DOPS appears to

decrease with increasing DOPS mole fraction.

Langmuir, 2016, 32 (39), pp 10083–10092




Figure 1A the compositional dependence of the c0, ± 7.5% error, of DOPS in water (black circles) and

13 mM [M2+] buffer (grey circles); 1B the compositional dependence of the c0, ± 7.5% error, of DOPS

in 65 mM [M2+] buffer (black squares) and 130 mM [M2+] buffer (grey squares).

A similar set of trends is also observed for the dependence of the c0 of DOPA in at different

concentrations of divalent cations (Figures 2A and 2B).

Figure 2A the compositional dependence of the c0, ± 7.5% error, of DOPA in water (black circles) and

13mM [M2+] buffer (grey circles); 2B the compositional dependence of the c0, ± 7.5% error, of DOPA

in 65mM [M2+] buffer (black squares) and 130mM [M2+] buffer (grey squares).

Langmuir, 2016, 32 (39), pp 10083–10092




Taken together our estimates of c0 for DOPS and DOPA suggest that the value of the spontaneous

curvature of anionic lipids is highly dependent both on their concentration in a binary mixture and

on the ionic strength of the buffer used to hydrate the HII phase. This complex behavior may be

rationalized by noting that as the amount of DOPS or DOPA in the mixture increases, the

electrostatic repulsion between the anionic headgroups increases. This leads to an increase in the

area occupied by the headgroups, therefore promoting a less negative interfacial curvature. The

divalent cations Mg2+ and Ca2+ can also form bridges between the anionic lipids, which has an

opposite effect and makes the headgroup area smaller and thus the curvature becomes more

negative. Furthermore the sodium counterions of the DOPS and DOPA lipids could affect interfacial

curvature through screening the anionic charge at the interface. This has been highlighted in a

recent study, where the spontaneous curvature of DOPS in Ca2+ containing systems was found to be

dependent on the concentration of monovalent cations 46. Thus, ultimately, the c0 of an anionic lipid

at a particular composition of the binary mixture and concentration of cations will be the sum of

these processes. From this analysis it is reasonable to expect the spontaneous curvature to be

dependent on the cation: lipid ratio. Thus care has to be taken before one can unambiguously

correlate the c0 of anionic lipids to biological activity. There are several reports in the literature that

describe the effects of divalent cations on DOPA and it is well documented that divalent cations

induce more negative curvature in these anionic systems. Recent work by Chen et al.32 shows that

increasing the Ca2+ concentration in DOPE: DOPA mixtures (prepared in 10 mM HEPES at pH 7.2)

decreases the measured c0 of DOPA from -0.106 nm-1 in the absence of Ca2+ to -0.312 nm-1 in 100

mM Ca2+. The c0 values that emerge from our models are also negative, but assume more negative

values of -0.4 nm-1. The difference between these values might stem from differences in the amount

of DOPE (3-9 wt% vs 10 wt% 32) or from different ratios of Ca2+ to DOPA between the two studies.

Since the method we use to determine the value of c0 is an estimate it is important to

question whether the different values of c0 we calculate for DOPS and DOPA are genuine or artefacts

of the estimate. To assess this we used our method to calculate c0 from data in the literature

detailing the temperature change of the lattice parameter of DOPE and DOPA mixtures, but

obtained when using a ‘traditional’ method to calculate the spontaneous curvature. To achieve this

we use the data of Chen et al. 32, who reconstruct the electron density of the inverse hexagonal

phase to determine the radius of the water cylinders (Rw) prior to determining c0 at the pivotal plane

for a number of different temperatures, DOPE: DOPA compositions and divalent cation

concentrations. In Figures S3 to S5 we contrast the values reported by Chen et al 32 to the values

obtained by our method but with their lattice parameter data; within error both techniques give the

Langmuir, 2016, 32 (39), pp 10083–10092




same c0 values as discussed section SI 1.2. This strongly suggests that the results shown in Figure 3A

and 3B are not artefacts of the methodology.

To further investigate this we modelled the equilibrium association of DOPS and DOPA with cations

and considered the resulting effects on the spontaneous curvature of DOPE: DOPA and DOPE: DOPS

lipid mixtures.

Modelling the equilibrium association of anionic lipids with cations and the resultant spontaneous

curvature

In order to assess quantitatively how the interactions between divalent cations and anionic

lipids might account for the trends in c0 that we observed experimentally, we set up a generic

equilibrium model of the different species. The model accounts for the ion exchange between the

sodium salt (LNa) of an anionic lipid and the salt (MX2) of a divalent cation. The generic lipid species

expected to occur at equilibrium, resulting from such an exchange process, would be: LNa, L-, LM+,

and L2M as shown in Table 3 and Figure S6A. The total spontaneous curvature of the equilibrium

mixture (c0 mix) resulting from a particular set of equilibrium constants is calculated from the

composition of the mixture by:

𝑐0 𝑚𝑖𝑥 = (1 − 𝑤 − 𝑥 − 𝑦 − 𝑧)𝑐0DOPE + 𝑤𝑐0LNa + 𝑥𝑐0L2M + 𝑦𝑐0LM+ + 𝑧𝑐0𝐿− (6)

We determined both the individual c0 values and the equilibrium constants that gave rise to the

concentrations w, x, y and z of LNa, L2M, LM+ and L- in the hexagonal phase through iterative

calculations selected for best fit to the experimental data. Table 3 shows the values of the

equilibrium constants and c0 for these mixtures.

Reaction Keq

(L = DOPA) Keq

(L = DOPS) Species

c0 (L = DOPA)

c0 (L = DOPS)

MX2 ⇌ M2+

+ 2X- 1.0x10

12 M

2 1.0x10

12 M

2 LNa -0.33 (±0.03) -0.22 (±0.02)

NaX ⇌ Na+ + X

- 1.0x10

12 M 1.0x10

12 M L

- -0.28 (±-0.03) -0.20 (±0.02)

L2M ⇌ L- + LM

+ 1.0(±0.7)x10

-8 M 1.0(±0.7)x10

-8 M LM

+ -0.29 (±0.03) -0.15 (±0.02)

LM+ ⇌ L

- + M

2+ 1.67(±0.20)x10

-8 M 2.0(±0.2)x10

-8 M L2M -1.70 (±0.12) -1.30 (±0.10)

LNa ⇌ L- + Na

+ 2 M 2.00 M DOPE -0.365 -0.365

Langmuir, 2016, 32 (39), pp 10083–10092




Table 3 parameters used to fit the equilibria model of coexisting anionic lipid species to the

experimentally determined mixture curvature values. LNa denotes the sodium salt of the anionic

lipid (DOPA or DOPS), M2+ denotes a divalent cation (magnesium or calcium), X- is an anion

(chloride).

Figure 3 shows the fits of this model to the experimental data for DOPA and DOPS systems.

Figure 3 spontaneous curvatures of (A) DOPE:DOPA and (B) DOPE:DOPS mixtures as a function of the

ratio of divalent cations to anionic lipids. Circles denote data for lipid concentration of 1.3x10-7 moles

µL-1 (Mfj = 0.09) and triangles for 4.0x10-8 moles µL-1(Mfj = 0.03). Curves through the data points are

fits from the theoretical model of anionic lipid species equilibria. The horizontal dotted line denotes

the value of c0j for pure DOPE.

The data in Figure 3 show that our simple equilibrium model describes the change in the

spontaneous curvature of DOPE mixtures containing DOPS and DOPA, at different divalent cation:

anionic lipid ratios (Table 2). Figures S6B and S7 show how both the total spontaneous curvature and

individual spontaneous curvatures of each of the components in the lipid mixture change with

divalent cation concentration. This model highlights that increasing the relative concentration of

divalent cations to anionic lipids leads to a maximum in c0 for DOPA and, to a lesser extent, also for

Langmuir, 2016, 32 (39), pp 10083–10092




DOPS. The few available relevant literature data for dissociation constants are also in reasonable

agreement with the values obtained from our model. For example, literature values for the apparent

association constant for the reaction LNa ⇌ L- + Na+ in vesicle systems are of the order of 2 M 47,

where L is PS and measurements are made on a biological extract of bovine brain PS 44. Similarly,

other data suggest that the dissociation constant of PS with Ca2+ is of the order of 1x10-6 M. Both

association constant values are within 2 orders of magnitude of the values that we determined by

fitting the experimental data. This discrepancy is not surprising since in our model we don’t

distinguish between Mg2+ and Ca2+ and the dissociation equilibria in vesicle systems are unlikely to

be the same as those in inverse hexagonal systems at limiting hydration.

As a final test we used a ‘traditional’ method to calculate the c0 mix values from the lattice

parameter data we obtained for DOPE: DOPA and DOPE: DOPS mixtures but making use of the well-

established relationship between limiting hydration fraction Φw, radius of the water cylinder and

radius of the pivotal plane . We are able to do this because a number of literature studies have

determined the limiting hydration value for DOPE: DOPS and DOPE: DOPA lipid mixtures in water

and in the presence of divalent cations 20,24,32.These methodology is shown in the supporting

information (SI 1.3), however we found that the trends in c0 mix that we report in Figure 3 were also

apparent using this traditional approach, as best demonstrated by Figure S8.

Towards a phenomenological model for determining lipid spontaneous curvatures

We have determined a significant number of spontaneous curvature values for a range of

structurally different lipids. These findings inspired us to establish a phenomenological approach

that could be used to facilitate future spontaneous curvature estimates. This would be particularly

advantageous when making spontaneous curvature estimates of expensive lipids or those available

in limited amounts. Recognizing that the larger the difference between the spontaneous curvature

of a guest lipid and that of DOPE, the larger the change in the lattice parameter of the HII phase as a

function of composition, we define the ‘curvature power ‘of lipid j (j) as:

j = (Lp,PE(37) – Lp,j(37)) /xj (7).

Langmuir, 2016, 32 (39), pp 10083–10092




where Lp,j(37) is the lattice parameter, at 37 °C, of lipid j, Lp,PE(37) is the lattice parameter of DOPE and

xj is the mole fraction of j. A plot of c0, estimated using our approach, against j for all the lipids

reported here is shown in Figure 4, where the data points for MO, OA and diPhyPE are highlighted.

Figure 4 range of spontaneous curvatures determined from XRD data for the lipids MO, OA and

DiPhyPE.

Figures S9 to S711 show the same data with the each of the other guest lipids highlighted. The

universal curve can be fitted with the linear equation:

c0 = 0.0731 2 – 0.3694 . (8)

These plots allow us to construct a universal curve that can be used to estimate the c0j value

of a guest lipid directly from its effect on the lattice parameter of the inverse hexagonal phase of the

host DOPE. Whilst this phenomenological approach may not have the same the accuracy in

estimating c0 as the method we developed, it does have the advantage of not requiring lattice

parameter measurements to be made at different temperatures. This would speed up the

generation of c0 values, especially where the thermal stability of lipids is unclear, and eliminates one

Langmuir, 2016, 32 (39), pp 10083–10092




of the assumptions in our model, namely that c0 is invariant with temperature. We tested the

predictive ability of this universal curve on literature X-ray diffraction data that we had not

previously used in the development of this model. For example, Leikin et al. 22 have determined the

spontaneous curvature of 1,2-dioleoylglycerol (DOG) to be approximately -1.1 nm from DOPE: DOG

mixtures and report the structural parameters of the inverse hexagonal phase determined by X-ray

diffraction. Using Figure 4 as a calibration curve, in conjunction with the structural parameter data of

Leikin et al. 22 we determined the spontaneous radius of curvature of DOG to be -1.4 nm. The two

values are in good agreement, suggesting that a phenomenological approach based on the

‘curvature power’ of a lipid might be a convenient and accessible way of estimating the c0 values of

lipids. Using this method we estimate the radius of spontaneous curvature of α-tocopherol to be -

1.52 nm from the data of Bradford et al. 48, a tight curvature that is consistent with the observation

that α-tocopherol promotes the formation of Fd3m phases49. Similarly, we estimate the

spontaneous curvature of elaidic acid to be -1.56 nm from the data of Funari et al. 50 indicating that

it is also a Type II lipid.

Conclusions

In this paper we have validated our recently reported method for estimating the

spontaneous curvatures of lipids from the temperature dependent changes in the lattice parameter

of inverse hexagonal phases. Using the host lipid DOPE we determined the spontaneous curvatures

of over 50 different lipid sample mixtures in around 1 week, including sample preparation, X-ray

measurement and data analysis. It is apparent from the data we present here that our method is

precise enough to give confident c0j values to within a 5% to 10% error. The accuracy of our method

will however always be below that of high resolution X-ray diffraction studies, but these

investigations entail significant time to establish the true position of the pivotal or neutral surface.

Furthermore, for most biophysical studies of lipid-protein interactions 4,51 and computational models

8,9,52,53 that are based on spontaneous curvature and stored elastic energy the accuracy of our

approach is sufficient. We also note that in the case of DOPE, multiple estimates of c0 exist in the

literature, using a variety of X-ray diffraction methods (each of which quotes small errors in the

value of c0), there is a spread of c0 values from -0.43 nm-1 to -0.33 nm-1 (± 13% of the mean).

We have here also presented a simple approach, based in the concept of the ‘curvature

power’ of a lipid, which could be used to rapidly estimate the spontaneous curvature of guest lipids

in DOPE inverse hexagonal phases. Whilst this phenomenological method is less accurate than our

Langmuir, 2016, 32 (39), pp 10083–10092




temperature dependent method or other published methods 17 for determining c0 values, it is likely

to be useful when a rough estimate of c0 is required or when the availability and/ or stability of lipids

is a limiting factor.

Our findings rely on a number of key assumptions i.e. that the spontaneous curvature is

invariant with temperature and that ideal mixing exists between the host and guest lipids. It is

interesting to consider at what point these assumptions break down and more importantly how this

might be identified. In the case of ideal mixing it is anticipated that lateral domain formation will be

one instance where Eq. 5 is not valid. In theory the best way to identify problems of this nature is to

use different host molecules with the same guest to calculate the spontaneous curvature of the

guest. If different values for the spontaneous curvature are being obtained with different hosts then

it is an indication that the mixing might be non-ideal.

Supporting Information Available: [supplementary figures, mathematical derivation and lattice

parameter measurements of binary lipid inverse hexagonal phases]. This material is available free of

charge via the Internet at http://pubs.acs.org.

Competing Interests

The authors declare no competing interests.

Funding

DP and RJG gratefully acknowledge the award of studentships by Chemistry and by the University of

Southampton Life Sciences Interfaces Forum respectively. MAX-lab IV is acknowledged for the beam

time provided under proposals 20120231, 20120338 and 20130326. TN acknowledges financial

support from the Swedish Research Council. MKD acknowledges start-up and capital funding from

the School of Pharmacy and Biological Sciences, University of Brighton.

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Langmuir, 2016, 32 (39), pp 10083 10092 DOI: Received 21 August …20et%20al... · 2019-12-16 · Langmuir, 2016, 32 (39), pp 10083–10092 DOI: 10.1021/acs.langmuir.6b03098 Received